Of the last 26 super bowl appearances for QBs, 14 were made by former first-round picks, 6 by a sixth-rounder (all Tom Brady), 3 by third-rounders, and 3 by second-rounders.
You don't have to take a QB in the first round, but it helps a lot and is the most common way to get a good one.
What I never want them to do is trade multiple picks to move up to get one.